Baccarat Dragon 7 Counting

  1. Baccarat Dragon 7 Counting Worksheets
  2. How To Count Baccarat
  3. Baccarat Dragon 7 Card Counting
  4. Baccarat Dragon 7 Counting Sheet
  5. Baccarat Dragon 7 Counting Chart

This is called card counting baccarat side bet or baccarat insurance card counting. In the card counting baccarat tie bet, all cards except 9 have negative (-1) values. Only the 9s are worth 12 points. Here is a simple rotation: In the first hand, we get 3, 4 (-1 + – 1 = -2). The Dragon/Fortune 7 baccarat side bet (DF7) is simple to describe. This side bet pays 40-to-1 if the Banker’s three-card total of 7 wins the hand, otherwise the bet loses. Analysis of the wager consists of a straight forward cycle through all possible hands. The table below gives the analysis for eight decks.

  1. When the running count is 0, bet the Dragon-7 side bet. This count scheme simulates at a profit rate of +52% of a fixed bet per 8-deck shoe, when 16 cards are placed behind the cut card. You’ll get about 6.8 betting opportunities per shoe.
  2. The game has two additional options, the Dragon 7, a specific bet of a winning three-card 7 on the banker side, which pays 40-to-1 instead of pushing, and Panda 8, a bet of a winning three-card 8 on the player side, which pays 25-to-1. Chemin de fer is a version which first appeared in the late 19th century.

On This Page

Introduction

I first saw EZ Baccarat on July 3, 2004, at the Plaza in Las Vegas. Since then it has picked up many more placements and has become one of the most popular baccarat variants.

Rules

The rules followed standard baccarat except on the Banker bet: (1) all wins pay even money, and (2) if the banker wins with a three-card total of 7, then the banker bet will push. There are a couple of side bets added, the Dragon 7 and Panda 8, which are explained below.

The following table shows the possible outcomes of the Banker bet, based on eight decks. The lower right cell shows a house edge of 1.02%

Banker Bet

EventPaysCombinationsProbabilityReturn
Banker win (except on 3-card 7)12,179,619,555,108,8700.4360640.436064
Banker win on 3-card 70112,633,011,329,0240.0225340.000000
Tie0475,627,426,473,2160.0951560.000000
Player wins-12,230,518,282,592,2500.446247-0.446247
Total04,998,398,275,503,3601.000000-0.010183

Dragon 7

The Dragon 7 bets wins on a Banker winning three-card total of seven. The following table shows the probability and return of each event, based on eight decks. The lower right cell shows a house edge of 7.61%.

Counting

Dragon 7

EventPaysCombinationsProbabilityReturn
Win40112,633,011,329,0240.0225340.901353
Loss-14,885,765,264,174,3400.977466-0.977466
Total4,998,398,275,503,3601.000000-0.076113

Panda 8

The Panda 8 bets wins on a Player winning three-card total of eight. The following table shows the probability and return of each event, based on eight decks. The lower right cell shows a house edge of 10.19%.

Panda 8

EventPaysCombinationsProbabilityReturn
Win25172,660,763,262,9760.0345430.863580
Lose-14,825,737,512,240,3800.965457-0.965457
Total4,998,398,275,503,3601.000000-0.101876

Internal Links

  • Main baccarat page.
  • Baccarat appendix 6 — Other versions of commission free baccarat.
  • Baccarat side bets.
  • Card Counting the Dragon 7 Bet.
  • Card Counting the Panda 8 Bet.

Baccarat Dragon 7 Counting Worksheets

Written by:Michael Shackleford
  • Appendices
  • Baccarat Analysis
  • Miscellaneous

On This Page

Introduction

On This Page

I don't like to accept articles by other writers. Few writers out there freelance at the kinds of standards I expect of myself for this site. Until now, I believe the only outside page I have accepted is the one on Flip It, by Michael Bluejay.

However, when Eliot Jacobson mentioned he had found the Dragon Bet in EZ Baccarat easily countable I was eager to cover it. As far as I know this topic has never been covered before. So I was quite happy when Eliot agreed to share the results of his analysis with my readers. Enjoy! — Wizard

Card Counting the Dragon Side Bet in EZ Baccarat

By Eliot Jacobson Ph.D., © 2011

The Dragon Side Bet for EZ Baccarat is simple to describe. This side bet pays 40-to-1 if the dealer’s three-card total of 7 beats the player, otherwise the bet loses. Analysis of the wager consists of a straight forward cycle through all possible hands. Table 1 gives the analysis for eight decks, with the house edge of 7.611% appearing in the lower right cell.

Table 1

EZ Baccarat Dragon Side Bet

EventPaysCombinationsProbabilityReturn
Winning Dragon40112,633,011,329,0240.0225300.901350
Losing Dragon-14,885,765,264,174,3300.977470-0.977470
Total4,998,398,275,503,3601.000000-0.076110

I first considered if the Dragon Side Bet was susceptible to a card counting methodology several months back. Intuitively, it seemed as though the wager was more probable to hit if there was an excess of 7 and 10 valued cards in the deck. In this case, the dealer would be more likely to draw 10-10 and hit to a 10-10-7 = 7. Later, as I read several Internet discussion boards, it became clear that others thought as I did. The conclusions were that if there was any vulnerability at all, it would come when 7’s and 10’s were in excess in the remainder of the shoe. It turns out this is not the case. The Dragon Side Bet is vulnerable to a card counting methodology, but the answer is surprising.

The key is that in order for the player to win the Dragon bet, the dealer has to draw a third card. This requirement trumps everything else. The cards that keep the dealer from drawing that third card most often are the 8 and the 9. As these cards are removed from the shoe, the edge moves quickly towards the counter’s favor. An excess of smaller cards is also helpful. The cards 1-7 are each cards that can move the dealer’s final total to 7 if he draws. Determining which of these low cards result in a final total of 7 most often is the key.

The methodology used in this study is familiar. The overall house edge for the game dealt from eight decks is 7.611%. By removing each card in turn from an eight-deck shoe, its effect on the house edge can be determined. This allows card counting systems to be developed. After arriving at candidate systems, computer simulations are run to see if these systems can generate an edge in practice. If there is an edge, the question then becomes if this is significant enough to become an opportunity for the advantage player.

Table 2 shows the number of winning and losing hands that result from removing one card from an eight-deck shoe, along with the house edge after removing that card.

Table 2

How To Count Baccarat

House Edge by Card Removed

Card RemovedWinning DragonLosing DragonTotalHouse Adv.
1111,068,343,867,6484,815,237,648,815,9504,926,305,992,683,600-0.075620
2110,900,807,733,2484,815,405,184,950,3504,926,305,992,683,600-0.077010
3110,879,201,710,3364,815,426,790,973,2604,926,305,992,683,600-0.077190
4110,686,449,371,6484,815,619,543,311,9504,926,305,992,683,600-0.078790
5110,691,915,602,5604,815,614,077,081,0404,926,305,992,683,600-0.078750
6110,618,934,007,2964,815,687,058,676,3004,926,305,992,683,600-0.079360
7110,577,900,912,8964,815,728,091,770,7004,926,305,992,683,600-0.079700
8111,654,703,169,5364,814,651,289,514,0604,926,305,992,683,600-0.070740
9111,583,436,417,5364,814,722,556,266,0604,926,305,992,683,600-0.071330
10111,112,191,215,1044,815,193,801,468,4904,926,305,992,683,600-0.075250

Table 2 allows us to compute the effect on the house edge for the Dragon bet by removing each card. Table 3 gives these results. The middle column (EOR) shows the change in house edge when the indicated card is removed. The final column (EOR x 1000) indicates potential card-counting tags to use in an optimal system.

Table 3

Effect of Removal

Card RemovedEOREOR x 1000
10.0005000.5
2-0.000900-0.9
3-0.001080-1.1
4-0.002680-2.7
5-0.002630-2.6
6-0.003240-3.2
7-0.003580-3.6
80.0053805.4
90.0047904.8
100.0008600.9

Table 3 indicates the extreme importance of ridding the shoe of 8’s and 9’s. Also, the 7 is the most important card, as expected, to remain in the shoe. The other cards diminish in value as their pips go down, presumably because they are used in fewer and fewer situations to draw to a dealer total of 7. Working against intuition, the counter’s situation improves as zero-valued cards are removed from the deck.

Looking at the values in the last column of Table 3, and adjusting slightly to make it balanced, we get card counting “system 1” with tags (0.5, -0.9, -1.1, -2.7, -2.7, -3.3, -3.6, 5.4, 4.8, 0.9). The reader will most likely consider it daunting to use system 1 in practice. However, as a baseline counting system, it is worthwhile to see how it performs. In an effort to simplify this unwieldy system as much as possible, I also considered the card counting system with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0). I’ll refer to this as “system 2.” This latter system is easily implemented by a counter of average skill level.

To gauge the effectiveness of each, I wrote a computer program to simulate using these two systems in live play. The game I simulated has the following shuffling and cut card rules:

  • The game is dealt from a shoe with 8 decks.
  • At the start of each shoe, a card is burned. Based on the value of the burn card, an additional number of cards are burned, equal to the value of the card.
  • The cut card is placed 14 cards from the end of the shoe.
  • After the cut card is dealt, one more round is dealt before shuffling.

Table 4 gives the results of a simulation of two hundred million (200,000,000) shoes.

Table 4

Simulation Results: 200M Shoes

ItemSystem 1System 2
Target Count104
Expected Value7.315%8.032%
Standard Deviation6.4566.567
Frequency of Bet10.698%9.163%
Units Won per Shoe0.63610.5967

Update: 10/14/2011. Shortly after this article was published, I realized that I had made an error that caused me to significantly underestimate the player advantage. This error was caused by using single-deck estimations for the remaining cards in the shoe, rather than determining the exact true count based on the fractional decks remaining. I revised my simulation program and confirmed my updated results with Steve How of discountgambling.net. I apologize for any inconvenience I may have caused the reader.

Baccarat Dragon 7 Card Counting

It is clear from the last row of Table 4 that system 2, with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0), performs remarkably well in comparison to its optimal cousin.

The person who uses system 2 should make the Dragon bet whenever the true count is +4 or higher. If he does so, then on average he will have an 8.03% edge over the house each time he makes the bet. This counter will have the opportunity to make the Dragon bet at or above the target true count on 9.16% of his hands. Given that the average shoe yields about 80 hands, the counter should be able to make, on average, about seven Dragon bets per shoe with the edge.

In dollar terms, if the house allows a Dragon bet up to $100 (say), then on a per-shoe basis the counter will average about $59.67 profit. The counter will earn about $8.03 per $100 wagered on the Dragon bet.

Baccarat Dragon 7 Counting Sheet

It is worthwhile to check that the simulated results for system 2 make sense combinatorially. One way to get a +4 true count off the top is to remove eight 8’s and eight 9’s from the deck. This will leave 400 cards remaining in the eight-deck shoe, with a running count of +32, for a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.0227%. Using a single deck, one way to get a +4 true count is to remove one 8 and one 9 from the deck. This leaves 50 cards with a +4 running count, giving a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.3114%. Because the player is making the Dragon bet at a true count of +4 and above, not just at +4, these computations represent a secondary confirmation of the simulated results.

Cut card placement varies by casino, so it is worthwhile to investigate how the edge changes with the placement of the cut card. Table 5 gives statistics for all cut card placements from 14 cards to 52 cards, and then by half-deck increments up to four decks. A cut card placement at one deck, instead of at 14 cards, decreases the potential profit to the player by about 50%.

Table 5

Card Counting Statistics by Cut Card DepthExpand

Cut Card DepthTrigger CountHands per ShoeExpected ValueStandard DeviationBet FrequencyPercent of Shoes PlayedProfit per Shoe (units)Profit per Hour (60 hands)
12481.698.30%6.5759.31%67.31%0.6310.464
13481.488.15%6.5709.24%66.54%0.6130.451
14481.288.03%6.5679.16%65.81%0.5970.440
15481.087.87%6.5629.09%65.12%0.5800.429
16480.887.81%6.5609.02%64.47%0.5690.422
17480.677.67%6.5568.95%63.81%0.5540.412
18480.477.64%6.5558.87%63.14%0.5450.407
19480.277.48%6.5518.80%62.48%0.5280.395
20480.077.42%6.5498.73%61.80%0.5180.388
21479.867.37%6.5478.66%61.14%0.5100.383
22479.667.28%6.5458.58%60.51%0.4980.375
23479.467.20%6.5428.52%59.93%0.4870.368
24479.267.04%6.5388.45%59.35%0.4720.357
25479.057.03%6.5378.38%58.77%0.4660.353
26478.856.92%6.5348.32%58.20%0.4540.345
27478.656.88%6.5338.25%57.65%0.4460.340
28478.456.84%6.5328.18%57.13%0.4390.336
29478.246.75%6.5298.12%56.64%0.4290.329
30478.046.69%6.5278.05%56.12%0.4210.323
31477.846.61%6.5257.99%55.61%0.4110.317
32477.646.58%6.5247.92%55.06%0.4050.313
33477.436.49%6.5217.86%54.53%0.3950.306
34477.236.47%6.5217.80%53.99%0.3890.302
35477.036.38%6.5187.73%53.49%0.3800.296
36476.836.33%6.5177.67%53.00%0.3730.291
37476.626.22%6.5137.61%52.53%0.3630.284
38476.426.21%6.5137.55%52.06%0.3580.281
39476.226.18%6.5127.49%51.59%0.3530.278
40476.026.15%6.5117.43%51.13%0.3470.274
41475.816.10%6.5107.37%50.70%0.3400.269
42475.615.97%6.5067.31%50.29%0.3300.262
43475.416.05%6.5087.25%49.85%0.3300.263
44475.215.97%6.5067.19%49.40%0.3230.257
45475.005.92%6.5047.13%48.95%0.3170.253
46474.805.81%6.5017.07%48.48%0.3070.246
47474.605.80%6.5017.01%48.03%0.3040.244
48474.405.72%6.4986.95%47.60%0.2960.239
49474.195.68%6.4976.90%47.19%0.2910.235
50473.995.68%6.4976.84%46.77%0.2870.233
51473.795.63%6.4966.78%46.36%0.2820.229
52473.595.62%6.4956.73%45.95%0.2780.227
1.5 decks468.324.79%6.4705.37%36.51%0.1760.154
2 decks463.064.16%6.4514.20%28.71%0.1100.105
2.5 decks457.793.64%6.4363.19%22.09%0.0670.070
3 decks452.533.22%6.4232.34%16.44%0.0390.045
3.5 decks447.273.13%6.4201.62%11.70%0.0240.030
4 decks442.002.74%6.4091.05%7.79%0.0120.017

This analysis shows that in theory the Dragon Side Bet in EZ Baccarat is an advantage play opportunity using a card counting methodology. In my opinion, however, given the high variance and low return, card counting is not a practical threat to the game.

About the Author

Baccarat Dragon 7 Counting Chart

For more information on Eliot, or to contact him, visit http://ijmp.org/ .

Related Pages

Please also see my own card counter vulnerability study of the Panda 8 side bet in EZ Baccarat.
Written by:Michael Shackleford
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